arXiv subjects

Chen Xuan

Publications and source records attributed to Chen Xuan.

6 recordsLinked to original sources

arXiv2020

Optimal Ternary Linear Complementary Dual Codes

Linear complementary dual (LCD) codes introduced by Massey are the codes whose intersections with their dual codes are trivial. It can help to improve the security of the information processed by sensitive devices, especially against side-channel attacks (SCA) and fault invasive attacks. In this paper, By construction of puncturing, extending, shortening and combination codes, many good ternary LCD codes are presented. We give a Table 1 with the values of $d_{LCD}(n,k)$ for length $ n \leq 20$. In addition, Many of these ternary LCD codes given in this paper are optimal which are saturating the lower or upper bound of Grassl's codetable in \cite{Grassl} and some of them are nearly optimal.

cs.IT↗

arXiv2017

The Plateau-Rayleigh instability in solids is a simple phase separation

A long elastic cylinder, radius $a$ and shear-modulus $μ$, becomes unstable given sufficient surface tension $γ$. We show this instability can be simply understood by considering the energy, $E(λ)$, of such a cylinder subject to a homogenous longitudinal stretch $λ$. Although $E(λ)$ has a unique minimum, if surface tension is sufficient ($Γ\equivγ/(aμ)>\sqrt{32}$) it looses convexity in a finite region. We use a Maxwell construction to show that, if stretched into this region, the cylinder will phase separate into two segments with different stretches $λ_1$ and $λ_2$. Our model thus explains why the instability has infinite wavelength, and allows us to calculate the instability's sub-critical hysteresis loop (as a function of imposed stretch), showing that instability proceeds with constant amplitude and at constant (positive) tension as the cylinder is stretched between $λ_1$ and $λ_2$. We use full nonlinear finite-element calculations to verify these predictions, and to characterize the interface between the two phases. Near $Γ=\sqrt{32}$ the length of such an interface diverges introducing a new length-scale and allowing us to construct a 1-D effective theory. This treatment yields an analytic expression for the interface itself, revealing its characteristic length grows as $l_{wall}\sim a/\sqrt{Γ-\sqrt{32}}$.

cond-mat.soft↗

arXiv2016

Finite wavelength surface-tension driven instabilities in soft solids, including instability in a cylindrical channel through an elastic solid

We deploy linear stability analysis to find the threshold wavelength ($λ$) and surface tension ($γ$) of Rayleigh-Plateau type "peristaltic" instabilities in incompressible neo-Hookean solids in a range of cylindrical geometries with radius $R_0$. First we consider a solid cylinder, and recover the well-known, infinite wavelength instability for $γ\ge6 μR_0$, where $μ$ is the solid's shear modulus. Second, we consider a volume-conserving (e.g.\ fluid filled and sealed) cylindrical cavity through an infinite solid, and demonstrate infinite wavelength instability for $γ\ge 2 μR_0$. Third, we consider a solid cylinder embedded in a different infinite solid, and find a finite wavelength instability with $λ\propto R_0$, at surface tension $γ\propto μR_0$, where the constants depend on the two solids' modulus ratio. Finally, we consider an empty cylindrical channel (or filled with expellable fluid) through an infinite solid, and find an instability with finite wavelength, $λ\approx2 R_0$, for $γ\ge 2.543... μR_0$. Using finite-strain numerics, we show such a channel jumps at instability to a highly peristaltic state, likely precipitating it's blockage or failure. We argue that finite wavelengths are generic for elasto-capillary instabilities, with the simple cylinder's infinite wavelength being the exception rather than the rule.

cond-mat.soft↗

arXiv2016

Exploring the cylindrical photo-bending shape in polydomain nematic glass

This paper explores different photo-bending shapes in polydomain nematic glass. The motivation is to explain the phenomenon in experiment [1] under polarized light in which a nematic film curls into an circular arc, like part of a cylindrical surface. Polarized light triggers photo-isomerization and therefore makes liquid crystals (LCs) contract along their directors. We apply the Sachs limit to homogenize the deformation of polydomain LC glass. Photo-strain can be either contraction or expansion through the material. Bending shapes can be anticlastic, bowl-shaped and cylindrical affected by Poisson ratio and illumination intensity. An explanation for the cylindrical bend and ways to observe other shapes are given in a parameter plane.

cond-mat.mtrl-sci↗

arXiv2016

Polarization dependence of photo-mechanical behavior of monodomain liquid crystal polymeric materials

Polarization dependence of opto-mechanical behavior of monodomain photochromic glassy liquid crystal (LC) polymers under polarized ultraviolet light (PUV) is studied. Trans-cis photo-isomerization is generally known to be most intense at 'parallel illumination' (polarization parallel to LC director), as light-medium interactions are active when polarization aligns with trainsition dipole moment. We show that at parallel illumination though cis isomers are converted from trans the most near surface, they can be the least below certain light propagation depth. Membrane force, an average effect of trans-cis conversion over propagation depths, shows a monotonic polarization dependence, i.e. maximum at parallel illumination, which agrees well with experiment [1]. However, under strong illumination, cis fraction/photo-contraction distribution through depths shows deep penetration, switching over the polarization dependence in photo-moment, which is related to photo-contraction gradient ---- photo-moment can be maximum at 'perpendicular illumination' (polarization perpendicular to director) under strong light. We give both intuitive explanation and analytical demonstration in thin strip limit for the switchover.

cond-mat.soft↗

arXiv2015

Deep optical penetration dynamics in photo-bending

We model both the photo-stationary state and dynamics of an illuminated, photo-sensitive, glassy liquid crystalline sheet. To illustrate the interplay between local tilt $θ$ of the sheet, effective incident intensity, curvature and dynamics, we adopt the simplest variation of local incident light intensity with angle, that is $\cosθ$. The tilt in the stationary state never overshoots the vertical, but maximum curvature could be seen in the middle of the sheet for intense light. In dynamics, overshoot and self-eclipsing arise, revealing how important moving fronts of light penetration are. Eclipsing is qualitatively as in the experiments of Ikeda and Yu (2003).

cond-mat.soft↗